where \(f_Y(\cdot )\)  are the universal scaling functions, and \(\delta t_c=t_c - \bar{t}_c(\infty )\) . The size of the largest gap \(\Delta \)  in the order parameter, as the maximum of random variables drawn from independent realizations of the entire percolation process, and the corresponding size of the largest cluster \(S^{\pm }_c\)  which dominates the system at \(t_c\) , can be viewed as the extreme events whose distributions are predicted by the extreme-value theory [1]}.
The critical threshold \(t_c\) , on the other hand, is a non-extremal variable drawn and averaged from independent realizations. Therefore, according to the central limit theorem, we expect a Gaussian distribution for \(t_c\) .
